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Understanding Geometry: Interior & Exterior Angles, Symmetry, and Polygon Types

Learn about interior and exterior angles in geometry, types of polygons like regular and irregular, symmetry concepts, and common polygon shapes. Explore the properties of shapes, angles inside triangles and squares, and classifications of polygons. Understand parallel lines, transversals, and angle relationships in polygons.

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Understanding Geometry: Interior & Exterior Angles, Symmetry, and Polygon Types

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  1. Geometry

  2. Glossary of terms • Interior angle: • Exterior angle: • Regular polygon: • Irregular polygon: • Symmetry

  3. Glossary of terms • Interior angle: An angle on the inside of a shape • Exterior angle: An angle on the outside of a shape • Regular polygon: A polygon that has all its faces the same shape and size • Irregular polygon: Its faces are different in shape and/or size • Symmetry: A shape that is in proportion and balance

  4. Interior and exterior angles Exterior angle Interior angles

  5. Shapes and Angles Q. What degree of angle does a straight line equal? A. The angles on any straight line add up to 180° Exterior angle Interior angle 90° 90° 90° + 90° = 180° Exterior angle Interior angle 135° 45° 135° + 45° = 180°

  6. Angles on parallel lines • A line that intersects (crosses) parallel lines creates angles. This line is called a transversal • The angles created are either: • Corresponding to each other • Alternate to each other or • Co-interior to each other (co-interior angles add up to 180°)

  7. Parallel lines and angles Corresponding angles = are the same Alternate angles = are the same Co-interior angles = add up to 180°

  8. Remember • The interior and exterior angle always add up to 180° ext int ext ext int int

  9. Angles inside a triangle • The angles inside a triangle also add up to 180° X° + 67° + 33° = 180° X° = 80° x° 33° 67°

  10. Angles inside a square • A square has four 90° angles that add up to 360°

  11. Polygons • Polygons are closed figures that have several line segments and angles(Poly = many; gonia = angle). •  Triangles are polygons with three sides. • Quadrilaterals are polygons that have four sides (quattuor = four, lateralis = side).  

  12. Some of the quadrilaterals are so special that they have they own names.

  13. Common Polygons • Parallelogramshave their oppositesides parallel. In rectanglesall the angles areright angles.

  14. More common polygons • A square has fourright angles and allsides are equal • Pentagons have 5 sides and 5 angles(pente = five, gonia = angle). regular irregular

  15. Even more common polygons • Hexagons have 6 sides and 6 angles(hex = six). regular regular or Irregular? irregular

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